Abstract
Time delay lensing is a mature and competitive cosmological probe. However, it is limited in accuracy by the well-known problem of the mass-sheet degeneracy: too rigid assumptions on the ...density profile of the lens can potentially bias the inference on cosmological parameters. I investigate the degeneracy between the choice of the lens density profile and the inference on the Hubble constant, focusing on double image systems. By expanding lensing observables in terms of the local derivatives of the lens potential around the Einstein radius, and assuming circular symmetry, I show that 3 degrees of freedom in the radial direction are necessary to achieve a few per cent accuracy in the time-delay distance. Additionally, while the time delay is strongly dependent on the second derivative of the potential, observables typically used to constrain lens models in time-delay studies, such as image position and radial magnification information, are mostly sensitive to the first and third derivatives, making it very challenging to accurately determine time-delay distances with lensing data alone. Tests on mock observations show that the assumption of a power-law density profile results in a 5 per cent average bias on H0, with a 6 per cent scatter. Using a more flexible model and adding unbiased velocity dispersion constraints allows me to obtain an inference with 1 per cent accuracy. A power-law model can still provide 3 per cent accuracy if velocity dispersion measurements are used to constrain its slope. Although this study is based on the assumption of axisymmetry, its main findings can be generalized to cases with moderate ellipticity.
Context. Time-delay lensing is a powerful tool for measuring the Hubble constant H0. However, in order to obtain an accurate estimate of H0 from a sample of time-delay lenses, very good knowledge of ...the mass structure of the lens galaxies is needed. Strong lensing data on their own are not sufficient to break the degeneracy between H0 and the lens model parameters on a single object basis. Aims. The goal of this study is to determine whether it is possible to break the H0-lens structure degeneracy with the statistical combination of a large sample of time-delay lenses, relying purely on strong lensing data with no stellar kinematics information. Methods. I simulated a set of 100 lenses with doubly imaged quasars and related time-delay measurements. I fitted these data with a Bayesian hierarchical method and a flexible model for the lens population, emulating the lens modelling step. Results. The sample of 100 lenses on its own provides a measurement of H0 with 3% precision, but with a −4% bias. However, the addition of prior information on the lens structural parameters from a large sample of lenses with no time delays, such as that considered in Paper I, allows for a 1% level inference. Moreover, the 100 lenses allow for a 0.03 dex calibration of galaxy stellar masses, regardless of the level of prior knowledge of the Hubble constant. Conclusions. Breaking the H0-lens model degeneracy with lensing data alone is possible, but 1% measurements of H0 require either many more than 100 time-delay lenses or knowledge of the structural parameter distribution of the lens population from a separate sample of lenses.
ABSTRACT
We investigate the internal structure of elliptical galaxies at z ∼ 0.2 from a joint lensing–dynamics analysis. We model Hubble Space Telescope images of a sample of 23 galaxy–galaxy lenses ...selected from the Sloan Lens ACS (SLACS) survey. Whereas the original SLACS analysis estimated the logarithmic slopes by combining the kinematics with the imaging data, we estimate the logarithmic slopes only from the imaging data. We find that the distribution of the lensing-only logarithmic slopes has a median 2.08c ± 0.03 and intrinsic scatter 0.13 ± 0.02, consistent with the original SLACS analysis. We combine the lensing constraints with the stellar kinematics and weak lensing measurements, and constrain the amount of adiabatic contraction in the dark matter (DM) haloes. We find that the DM haloes are well described by a standard Navarro–Frenk–White halo with no contraction on average for both of a constant stellar mass-to-light ratio (M/L) model and a stellar M/L gradient model. For the M/L gradient model, we find that most galaxies are consistent with no M/L gradient. Comparison of our inferred stellar masses with those obtained from the stellar population synthesis method supports a heavy initial mass function (IMF) such as the Salpeter IMF. We discuss our results in the context of previous observations and simulations, and argue that our result is consistent with a scenario in which active galactic nucleus feedback counteracts the baryonic-cooling-driven contraction in the DM haloes.
Abstract
We present a Bayesian hierarchical inference formalism to study the relation between the properties of dark matter haloes and those of their central galaxies using weak gravitational ...lensing. Unlike traditional methods, this technique does not resort to stacking the weak lensing signal in bins, and thus allows for a more efficient use of the information content in the data. Our method is particularly useful for constraining scaling relations between two or more galaxy properties and dark matter halo mass, and can also be used to constrain the intrinsic scatter in these scaling relations. We show that, if observational scatter is not properly accounted for, the traditional stacking method can produce biased results when exploring correlations between multiple galaxy properties and halo mass. For example, this bias can affect studies of the joint correlation between galaxy mass, halo mass, and galaxy size, or galaxy colour. In contrast, our method easily and efficiently handles the intrinsic and observational scatter in multiple galaxy properties and halo mass. We test our method on mocks with varying degrees of complexity. We find that we can recover the mean halo mass and concentration, each with a 0.1 dex accuracy, and the intrinsic scatter in halo mass with a 0.05 dex accuracy. In its current version, our method will be most useful for studying the weak lensing signal around central galaxies in groups and clusters, as well as massive galaxies samples with log M* > 11, which have low satellite fractions.
Abstract
Early-type galaxies provide unique tests for the predictions of the cold dark matter cosmology and the baryonic physics assumptions entering models for galaxy formation. In this work, we use ...the Illustris simulation to study correlations of three main properties of early-type galaxies, namely the stellar orbital anisotropies, the central dark matter fractions and the central radial density slopes, as well as their redshift evolution since z = 1.0. We find that lower mass galaxies or galaxies at higher redshift tend to be bluer in rest-frame colour, have higher central gas fractions, and feature more tangentially anisotropic orbits and steeper central density slopes than their higher mass or lower redshift counterparts, respectively. The projected central dark matter fraction within the effective radius shows a very mild mass dependence but positively correlates with galaxy effective radii due to the aperture effect. The central density slopes obtained by combining strong lensing measurements with single-aperture kinematics are found to differ from the true density slopes. We identify systematic biases in this measurement to be due to two common modelling assumptions, isotropic stellar orbital distributions and power-law density profiles. We also compare the properties of early-type galaxies in Illustris to those from existing galaxy and strong lensing surveys; we find in general broad agreement but also some tension, which poses a potential challenge to the stellar formation and feedback models adopted by the simulation.
We investigate the cosmic evolution of the internal structure of massive early-type galaxies over half of the age of the universe. We perform a joint lensing and stellar dynamics analysis of a sample ...of 81 strong lenses from the Strong Lensing Legacy Survey and Sloan ACS Lens Survey and combine the results with a hierarchical Bayesian inference method to measure the distribution of dark matter mass and stellar initial mass function (IMF) across the population of massive early-type galaxies. Lensing selection effects are taken into account. We find that the dark matter mass projected within the inner 5 kpc increases for increasing redshift, decreases for increasing stellar mass density, but is roughly constant along the evolutionary tracks of early-type galaxies. The average dark matter slope is consistent with that of a Navarro-Frenk-White profile, but is not well constrained. The stellar IMF normalization is close to a Salpeter IMF at log M * = 11.5 and scales strongly with increasing stellar mass. No dependence of the IMF on redshift or stellar mass density is detected. The anti-correlation between dark matter mass and stellar mass density supports the idea of mergers being more frequent in more massive dark matter halos.
We present optical and near-infrared spectroscopy obtained at Keck, Very Large Telescope, and Gemini for a sample of 36 secure strong gravitational lens systems and 17 candidates identified as part ...of the Strong Lensing Legacy Survey. We combine these data with photometric and lensing measurements presented in the companion paper III and with lenses from the Sloan Lens Advanced Camera for Surveys and Lenses Structure and Dynamics surveys to investigate the cosmic evolution of the internal structure of massive early-type galaxies over half the age of the universe. This result is obtained by combining our measured dependencies of gamma ' on z, M sub(*), R sub(eff) with the evolution of the R sub(eff)-M sub(*) taken from the literature, and is broadly consistent with current models of the formation and evolution of massive early-type galaxies. Detailed quantitative comparisons of our results with theory will provide qualitatively new information on the detailed physical processes at work.
The initial mass function (IMF) for massive galaxies can be constrained by combining stellar dynamics with strong gravitational lensing. However, this method is limited by degeneracies between the ...density profile of dark matter and the stellar mass-to-light ratio (M/L). In this work, we reduce this degeneracy by combining weak lensing together with strong lensing and stellar kinematics. Our analysis is based on two galaxy samples: 45 strong lenses from the SLACS survey and 1700 massive quiescent galaxies from the Sloan Digital Sky Survey main spectroscopic sample with weak lensing measurements from the Hyper Suprime-Cam survey. We use a Bayesian hierarchical approach to jointly model all three observables. We fit the data with models of varying complexity and show that a model with a radial gradient in the stellar M/L is required to simultaneously describe both galaxy samples. This result is driven by a subset of strong lenses with very steep total density profile that cannot be fitted by models with no gradient. Our measurements are unable to determine whether gradients are due to variations in stellar population parameters at fixed IMF, or to gradients in the IMF itself. The inclusion of M_*/L gradients decreases dramatically the inferred IMF normalization, compared to previous lensing-based studies, with the exact value depending on the assumed dark matter profile. The main effect of strong lensing selection is to shift the stellar mass distribution towards the high-mass end, while the halo mass and stellar IMF distribution at fixed stellar mass are not significantly affected.
We present Hubble Space Telescope (HST) imaging data and Canada-France-Hawaii Telescope (CFHT) near-infrared ground-based images for the final sample of 56 candidate galaxy-scale lenses uncovered in ...the CFHT Legacy Survey as part of the Strong Lensing in the Legacy Survey project. Based on the analysis of systematic uncertainties and comparison with inference based on different methods, we estimate that our Einstein radii are accurate to ~3%. HST imaging provides a much higher success rate in confirming gravitational lenses and measuring their Einstein radii than CFHT imaging does. Lens modeling with ground-based images, however, when successful, yields Einstein radius measurements that are competitive with space-based images. The redshifts of the main deflector span a range 0. 3 < or =, slant z sub(d) < or =, slant 0.8, which nicely complements low-redshift samples like the Sloan Lens ACS survey and thus provides an excellent sample for the study of the cosmic evolution of the mass distribution of ETGs over the second half of the history of the universe.
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